Math Placement Exam Practice Problems
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1
2√
11. Beginning with the function f (x) =
x, find
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the function g(x) that shows f (x) shifted to the
MPE2 Math Placement Exam
left 2 units, reflected about the x-axis, and then
Practice Problems
shifted up 7 units.
12. Solve for x in the inequality.
1. Rationalize the denominator.
14
x + 2
(5x
10) ≥ 3
√
3 +
2
13. Find the domain of
2. Find the sum or difference as indicated and
2
x
3x
2
write your answer in simplified form.
f (x) =
2
6x
54
x + 2a
3
x + 6
.
x + a
2x
14. Find the domain of the function
3. Factor and reduce to simplest form.
2
2x
+ 13
, x < 0
2
2
6x
+ 11xy
10y
2
x
1
f (x) =
2
2
3x
+ 10xy
8y
5x
26
,
x ≥ 0
4. Solve the following equation.
x + 2
.
5(x
7)
13(x
7)
6 = 0
15. Find the x- and y-intercepts of the function 2x+
3y = 10, if any exist.
5. Find the point (x,y) which satisfies both equa-
tions. What is the value of x + y?
16. Simplify the expression and then write your an-
swer using positive rational exponents.
2x + 4y = 12
3x
5y =
3
√
2
3
4x
√
5
x
2
17. If we begin with the graph of f (x) = x
and
6. Two investments are made, totaling $10,000. In
shift f (x) 4 units to the right, shrink f (x) ver-
one year, these investments yield $650 in simple
1
, and then shift f (x) up-
1
tically by a factor of
interest. Part of the $10,000 is invested at 5
%,
2
2
wards 10 units, write the equation for the trans-
3
and the rest at 6
%. How much more money is
4
formed graph.
3
invested at 6
%?
4
18. Find f ◦ g (also denoted f (g(x))) if f (x) =
7. Given the linear equation 2ax + 3by = 7c,
x
2
where a, b and c > 0, if x decreases by 10 units,
and g(x) =
. Simplify.
x + 1
x
what is the corresponding change in y?
19. Write the following inequalities in interval no-
8. Perform the indicated operations and simplify.
tation.
8
y
y
4
(a) x ≥ 2
÷
x + 1
z + 2
w
(b)
4 ≤ x < 7
(c) x <
5
9. Find the equation of the line passing through the
point (5,1) with a slope of 7. Use the equation
(d) All x such that x is a real number.
you find to determine the value of y when x =
20. Write the following intervals using inequality
4.
notation.
10. Line A passes through the points (2k+3, 4k 6)
(a) [0, 2)
and ( 2, 16). Find the value of k if line A has
a slope of 0.
(b) ( ∞, 4)
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